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arxiv: 2606.22642 · v1 · pith:PZRKDXYKnew · submitted 2026-06-21 · ✦ hep-ph · hep-th

Radiative Lifting of mathbb{Z}₃ Domain-Wall Degeneracy in a Type-III Seesaw Model: Implications for Leptogenesis and Gravitational Waves

Priya , Labh Singh , B. C. Chauhan , Surender Verma This is my paper

Pith reviewed 2026-06-26 09:54 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords Z3 symmetrytype-III seesawdomain wallsColeman-Weinberg potentialleptogenesisgravitational wavesneutrino massesradiative corrections
0
0 comments X

The pith

Radiative corrections lift degeneracy among Z3 vacua in a type-III seesaw model, causing domain walls to annihilate.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines a Z3-symmetric extension of the Standard Model with three hyperchargeless SU(2)L fermion triplets generating neutrino masses via the type-III seesaw and a complex scalar singlet breaking the Z3 symmetry through its vacuum expectation value. Radiative corrections from the Yukawa interactions between the triplets and the singlet produce a Coleman-Weinberg effective potential that biases the three vacua and lifts their degeneracy, triggering annihilation of the resulting unstable domain walls. The same setup generates the observed baryon asymmetry through thermal leptogenesis from out-of-equilibrium decays of the lightest triplet at masses around 10^9 GeV and yields a gravitational-wave spectrum that can lie within the sensitivity of future detectors, all while remaining consistent with neutrino oscillation data via numerical scans.

Core claim

The Yukawa interactions between the SU(2)_L fermion triplets and the complex scalar singlet χ induce radiative corrections that generate a Coleman-Weinberg effective potential. This potential creates a dynamical bias term lifting the degeneracy among the three Z3 vacua, which triggers the annihilation of unstable domain walls. The framework simultaneously explains neutrino masses, produces the observed baryon asymmetry via leptogenesis, and yields a gravitational-wave spectrum within reach of future detectors.

What carries the argument

The Coleman-Weinberg effective potential generated by the Yukawa couplings between the fermion triplets and the scalar singlet, which supplies the vacuum bias term that destabilizes the domain walls.

If this is right

  • Domain walls annihilate before dominating the energy density of the universe.
  • The baryon asymmetry arises from thermal leptogenesis via decays of the lightest fermion triplet at O(10^9) GeV.
  • The gravitational-wave spectrum from domain-wall annihilation or the associated phase transition falls within reach of space-based and ground-based detectors for suitable parameter choices.
  • Viable regions of parameter space exist that reproduce current neutrino masses and mixing angles.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same radiative-bias mechanism could resolve domain-wall issues in other beyond-Standard-Model constructions that employ discrete symmetries.
  • Future gravitational-wave observations in specific frequency windows could indirectly constrain the Yukawa couplings and the mass of the lightest triplet.
  • The setup links the scale of neutrino mass generation directly to early-universe dynamics through the size of the bias term.

Load-bearing premise

The Yukawa interactions and parameter choices must produce a Coleman-Weinberg bias large enough to trigger domain wall annihilation on cosmologically relevant timescales while fitting neutrino data and leptogenesis requirements.

What would settle it

Cosmological evidence for long-lived stable domain walls persisting to late times, or non-observation of the predicted gravitational-wave spectrum in the bands accessible to future detectors, or inability to match the baryon asymmetry with triplet masses near 10^9 GeV under the required Yukawa couplings.

Figures

Figures reproduced from arXiv: 2606.22642 by B. C. Chauhan, Labh Singh, Priya, Surender Verma.

Figure 1
Figure 1. Figure 1: FIG. 1: Correlation among the neutrino mixing angles, CP invariants( [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Evolution of the comoving number density of the lightest fermion triplet [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Gravitational wave peak amplitude as a function of the peak frequency for the selected [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The gauge interactions (left panel) and inverse decay (right panel) rate as function of [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
read the original abstract

In this work, we study a $\mathbb{Z}_3$-symmetric extension of the Standard Model with three hyperchargeless $SU(2)_L$ fermion triplets responsible for neutrino mass generation $\textit{via}$ the Type-III seesaw mechanism together with a complex scalar singlet $\chi$ whose vacuum expectation value spontaneously breaks the $\mathbb{Z}_3$ symmetry. Radiative corrections induced by the Yukawa interactions between the $SU(2)_L$ fermion triplets and the complex scalar singlet $\chi$ generate a Coleman-Weinberg vacuum bias that lifts the degeneracy among the $\mathbb{Z}_3$ vacua, leading to the annihilation of unstable domain-walls. Consequently, the degeneracy among the $\mathbb{Z}_3$ vacua is lifted radiatively through the Coleman-Weinberg effective potential, generating a dynamical bias term that triggers the annihilation of unstable domain walls. We perform a numerical analysis consistent with current neutrino oscillation data and identify viable regions of parameter space accommodating the observed neutrino masses and leptonic mixing parameters. The observed baryon asymmetry of the Universe is generated through thermal leptogenesis $\textit{via}$ the out-of-equilibrium decay of the lightest fermion triplet for masses around $\mathcal{O}(10^{9})\,\mathrm{GeV}$, consistent with the Type-III seesaw framework. Depending on the choice of model parameters, the predicted gravitational-wave spectrum can fall within the sensitivity reach of future space-based and ground-based gravitational-wave detectors. Our framework therefore establishes a correlation between neutrino mass generation, leptogenesis, radiative domain-wall instability, and gravitational-wave phenomenology.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes a Z_3-symmetric Type-III seesaw model with three hypercharge-less SU(2)_L fermion triplets and a complex scalar singlet χ whose VEV breaks Z_3. It claims that Yukawa-induced one-loop Coleman-Weinberg corrections generate a vacuum bias lifting the exact degeneracy among the three Z_3 vacua, triggering domain-wall annihilation. Viable parameter regions are identified that reproduce neutrino oscillation data; thermal leptogenesis proceeds via out-of-equilibrium decays of the lightest triplet at O(10^9) GeV, and the resulting gravitational-wave spectrum may be detectable by future interferometers.

Significance. If the central claim holds, the work would establish a concrete link between radiative lifting of discrete symmetry vacua, domain-wall cosmology, Type-III leptogenesis, and observable gravitational waves within a single renormalizable framework. The approach is standard in its use of Coleman-Weinberg potentials, but its impact hinges on whether the generated bias is demonstrably sufficient for cosmologically timely annihilation while remaining consistent with neutrino data and leptogenesis requirements.

major comments (2)
  1. [Abstract and radiative-corrections paragraph] The abstract and the paragraph describing the radiative corrections assert that the Coleman-Weinberg bias term is large enough to annihilate unstable domain walls on relevant timescales, yet the explicit one-loop effective potential, the resulting bias expression, and the numerical evaluation of its magnitude relative to the wall tension are not supplied. This calculation is load-bearing for the domain-wall instability claim and for the subsequent gravitational-wave prediction.
  2. [Numerical analysis section] The numerical analysis is stated to be consistent with neutrino oscillation data and to yield viable leptogenesis regions, but the scan procedure, the treatment of the free parameters (Yukawa couplings, triplet masses, scalar potential parameters), and any checks against over-tuning or post-hoc selection are not detailed. This directly affects the robustness of the claimed viable parameter space.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments. We address each major point below and will revise the manuscript to incorporate the requested details and clarifications.

read point-by-point responses

  1. Referee: [Abstract and radiative-corrections paragraph] The abstract and the paragraph describing the radiative corrections assert that the Coleman-Weinberg bias term is large enough to annihilate unstable domain walls on relevant timescales, yet the explicit one-loop effective potential, the resulting bias expression, and the numerical evaluation of its magnitude relative to the wall tension are not supplied. This calculation is load-bearing for the domain-wall instability claim and for the subsequent gravitational-wave prediction.

    Authors: We agree that the explicit one-loop Coleman-Weinberg effective potential, the derived bias term, and its numerical comparison to the domain-wall tension were not presented with sufficient detail in the current version. In the revised manuscript we will add the full analytic expression for the one-loop potential induced by the Yukawa interactions, the resulting bias ΔV, and a quantitative estimate showing that the bias is sufficient to trigger annihilation on cosmologically relevant timescales while remaining consistent with the gravitational-wave predictions. revision: yes

  2. Referee: [Numerical analysis section] The numerical analysis is stated to be consistent with neutrino oscillation data and to yield viable leptogenesis regions, but the scan procedure, the treatment of the free parameters (Yukawa couplings, triplet masses, scalar potential parameters), and any checks against over-tuning or post-hoc selection are not detailed. This directly affects the robustness of the claimed viable parameter space.

    Authors: We acknowledge that the description of the numerical scan is incomplete. In the revised version we will expand the numerical analysis section to specify the scan method (e.g., random or grid sampling), the ranges and priors assigned to the Yukawa couplings, triplet masses, and scalar potential parameters, and any explicit checks performed for fine-tuning or selection bias. This will strengthen the robustness of the reported viable regions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The supplied abstract and description outline a standard model construction: Z3 symmetry broken by a scalar singlet, with one-loop Coleman-Weinberg corrections from Yukawa couplings to fermion triplets generating a vacuum bias that lifts domain-wall degeneracy. Viable parameter regions are identified by scanning against neutrino oscillation data and requiring successful thermal leptogenesis, which is ordinary model-building practice rather than a reduction of any claimed prediction to its own inputs. No equations are quoted that equate a derived quantity to a fitted input by construction, no self-citation is invoked as a uniqueness theorem, and no ansatz is smuggled via prior work. The bias term is generated by explicit loop integrals whose magnitude depends on the same Yukawas constrained by data, but this dependence is physical and falsifiable rather than tautological. The framework therefore contains independent content linking neutrino masses, leptogenesis, domain-wall dynamics, and gravitational waves.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 3 invented entities

The central claim depends on introducing new particles and a discrete symmetry whose breaking is lifted by loops, plus multiple parameters adjusted to match low-energy data and cosmological observations.

free parameters (3)
  • lightest triplet mass
    Set near 10^9 GeV to produce the observed baryon asymmetry via thermal leptogenesis.
  • Yukawa couplings between triplets and scalar
    Adjusted to fit neutrino oscillation data and to generate the required radiative bias.
  • scalar potential parameters
    Chosen to allow spontaneous Z3 breaking while producing a viable effective potential.
axioms (3)
  • domain assumption The Type-III seesaw mechanism with three hyperchargeless SU(2)_L triplets generates the observed neutrino masses and mixings.
    Invoked in the abstract as the source of neutrino masses.
  • domain assumption Thermal leptogenesis via out-of-equilibrium decay of the lightest triplet produces the observed baryon asymmetry.
    Stated as the mechanism for baryon asymmetry generation.
  • standard math Standard quantum field theory loop corrections produce the Coleman-Weinberg effective potential.
    Used to generate the vacuum bias.
invented entities (3)
  • three hyperchargeless SU(2)_L fermion triplets no independent evidence
    purpose: Generate neutrino masses via Type-III seesaw and induce radiative corrections to the scalar potential.
    New particles added to the model; no independent evidence provided.
  • complex scalar singlet χ no independent evidence
    purpose: Spontaneously breaks the Z3 symmetry and receives radiative corrections from Yukawa interactions.
    New field introduced to break the symmetry and generate the bias; no independent evidence provided.
  • Z3 discrete symmetry no independent evidence
    purpose: Protects the model structure and leads to domain wall formation upon breaking.
    Imposed symmetry whose breaking creates the domain wall problem that is then solved radiatively.

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Reference graph

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